This is pretty neat... Having an interest in the space for many years (on-and-off; life gets busy sometimes) - I've often lamented the lack of good pixel-level performance optimizations in graphics cards. Everything seems hell-bent on polygons. Some years ago, DirectDraw on Windows was an excellent way to optimize the graphics portion of these types of things, but that all went away as "3D Is The Way" mentality took…
The thing you describe as "per-pixel optimizations" is exactly what a fragment shader is? You don't need "a polygon" per say, you can just run said code over ever pixel in the frame for each frame. This is how simple screenspace effects are implemented, compositing, HDR, etc.
I guess all that I'd need would be in-memory buffer of my field, then a single function to copy the buffer (or section of the buffer if I want larger than screen fields) to the video buffer.